Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 539.374 Doi: 10.31772/2712-8970-2021-22-1-8-17
Torsion of prismatic orthotropic elastoplastic rods
Burenin A. A., Senashov S. I., Savostyanova I. L.
Khabarovsk Federal Research Center of the Far Eastern Branch of the Russian Academy of Sciences, 51, Turgenev St., Khabarovsk, 680000, Russian Federation; Reshetnev Siberian State University of Science and Technology, 31, Krasnoiarskii Rabochi Prospekt, Krasnoyarsk, 660037, Russian Federation
Conservation laws were introduced into the theory of differential equations by E. Noether more than 100 years ago and are gradually becoming an important tool for the study of differential equations systems. Not only do they allow you to qualitatively investigate the equation, but, as the authors of this article show, they also enable you to find exact solutions to the boundary value problems. For the equations of the iso-tropic theory of elasticity, the conservation laws were first calculated by P. Olver. For the equations of the theory of plasticity in the two-dimensional case, the conservation laws were found by one of the authors of this article and used to solve the main boundary value problems of the plasticity equations. Later it turned out that the conservation laws can also be used to find the boundaries between elastic and plastic zones in twisted rods, bent beams, and deformable plates. The proposed work found conservation laws for equations describing the orthotropic elastic state of the twisted straight-line rod. It is assumed that the remaining current depends linearly on the voltage tensor component. In the workit was also found an endless series of laws of preservation, which allows you to find an elastic-plastic boundary, which arises when twisting the orthotropic rod.
Keywords: torsion of rods, boundary value problems, conservation laws
References

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Burenin Anatoly Aleksandrovich – Corresponding Member of the Russian Academy of Sciences, Dr. Sc., Professor; Chief Researcher of the Khabarovsk Federal Research Center of the Far Eastern Branch of the Russian Academy of Sciences. Tel.: +7 (4212) 32-79-27.

    Senashov Sergei Ivanovich – Dr. Sc., Professor, Head of the Department of IES; Reshetnev Siberian State University of Science and Technology. E-mail: sen@sibsau.ru.

Savostyanova Irina Leonidovna – Cand. Sc., Associate Professor of the Department of IES, Reshetnev Siberian State University of Science and Technology. E-mail: savostyanova@sibsau.ru.


  Torsion of prismatic orthotropic elastoplastic rods